Question: $J$ $K$ $L$ If: $ KL = 2x + 4$, $ JL = 31$, and $ JK = 4x + 3$, Find $KL$.
Answer: From the diagram, we can see that the total length of ${JL}$ is the sum of ${JK}$ and ${KL}$ $ {JK} + {KL} = {JL}$ Substitute in the expressions that were given for each length: $ {4x + 3} + {2x + 4} = {31}$ Combine like terms: $ 6x + 7 = {31}$ Subtract $7$ from both sides: $ 6x = 24$ Divide both sides by $6$ to find $x$ $ x = 4$ Substitute $4$ for $x$ in the expression that was given for $KL$ $ KL = 2({4}) + 4$ Simplify: $ {KL = 8 + 4}$ Simplify to find ${KL}$ : $ {KL = 12}$